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We develop a second order well-balanced finite volume scheme for compressibleEuler equations with a gravitational source term. The well-balanced propertyholds for arbitrary hydrostatic solutions of the corresponding Euler equationswithout any restriction on the equation of state. The hydrostatic solution mustbe known a priori either as an analytical formula or as a discrete solution atthe grid points. The scheme can be applied on curvilinear meshes and incombination with any consistent numerical flux function and time steppingroutines. These properties are demonstrated on a range of numerical tests.

Second order finite volume scheme for Euler equations with gravity which is well-balanced for general equations of state and grid systems